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Prove that there exist polynomials P and Q

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September 20, 2010
algebrapolynomialcoefficientsIMO Shortlist

Problem Statement

Let PP be a polynomial with real coefficients such that P(x)>0P(x) > 0 if x>0x > 0. Prove that there exist polynomials QQ and RR with nonnegative coefficients such that P(x)=Q(x)R(x)P(x) = \frac{Q(x)}{R(x)} if x>0.x > 0.
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